Solving an Exponential equation symbolically using Logarithms

**Etiennedv** · August 31st 2010, 04:07 PM

I've been working on this problem and I just can't seem to figure it out.

Solve the expression

for

assuming that all other letters are positive constants.

I just keep running into dead ends where I have t on both sides or both t's on one side.

**wonderboy1953** · August 31st 2010, 04:43 PM

What have you tried so far?

**pickslides** · August 31st 2010, 04:54 PM

Is this ok?

$\displaystyle Pa^t = Vg^t$

$\displaystyle \frac{P}{V} = \frac{g^t}{a^t}$

$\displaystyle \frac{P}{V} = \left(\frac{g}{a}\right)^t$

$\displaystyle t = \log_{\frac{g}{a}}\frac{P}{V}$

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